Abstract
In this paper, we discuss the arithmetic operations on fuzzy numbers from the point of view of Genuine set. The paper specially studies the operations on triangular fuzzy numbers and presents an effect algorithm to compute them. We divide one general triangular fuzzy number into two symmetric triangular fuzzy numbers by the properties of extension maximum and minimum operations for the convenience of the calculation.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Taheri, S.M.: C-fuzzy numbers and a dual of extension principle. Inform. Sci. 178, 827–835 (2008)
Huang, H.L., Shi, F.G.: L-fuzzy numbers and their properties. Inform. Sci. 178, 1141–1151 (2008)
Yeh, C.T.: A note on trapezoidal approximations of fuzzy numbers. Fuzzy Sets and Systems 158, 747–754 (2007)
Ban, A.: Approximation of fuzzy numbers by trapezoidal fuzzy numbers preserving the expected interval. Fuzzy Sets and Systems 159, 1327–1344 (2008)
Allahviranloo, T., Adabitabar, F.M.: Note on Trapezoidal approximation of fuzzy numbers. Fuzzy Sets and Systems 158, 755–756 (2007)
Grzegorzewski, P., Mrowka, E.: Trapezoidal approximations of fuzzy numbers—revisited. Fuzzy Sets and Systems 158, 757–768 (2007)
Grzegorzewski, P.: Trapezoidal approximations of fuzzy numbers preserving the expected interval—Algorithms and properties. Fuzzy Sets and Systems 159, 1354–1364 (2008)
Yeh, C.T.: On improving trapezoidal and triangular approximations of fuzzy numbers. Internat. J. Approx. Reason. 48, 297–313 (2008)
Yeh, C.T.: Trapezoidal and triangular approximations preserving the expected interval. Fuzzy Sets and Systems 159, 1345–1353 (2008)
Demirci, M., Waterman, M.S.: Genuine sets. Fuzzy Sets and Systems 105, 377–384 (1999)
Demirci, M.: Some notices on genuine sets. Fuzzy Sets and Systems 110, 275–278 (2000)
Coker, D., Demirci, M.: An invitation to topological structures on first order genuine sets. Fuzzy Sets and Systems 119, 521–527 (2001)
Demirci, M.: Genuine sets, various kinds of fuzzy sets and fuzzy rough sets. International Journal of Uncertainty. Fuzziness Knowledge-Based Systems 11(4), 467–494 (2003)
Demirci, M.: Generalized set-theoretic operations on genuine sets. Hacet. J. Math. Stat. 34S, 1–6 (2005)
Chiu, C.H., Wang, W.J.: A simple computation of MIN and MAX operations for fuzzy numbers. Fuzzy Sets and Systems 126, 273–276 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Han, J., Hu, B. (2010). Operations of Fuzzy Numbers via Genuine Set. In: Yu, J., Greco, S., Lingras, P., Wang, G., Skowron, A. (eds) Rough Set and Knowledge Technology. RSKT 2010. Lecture Notes in Computer Science(), vol 6401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16248-0_83
Download citation
DOI: https://doi.org/10.1007/978-3-642-16248-0_83
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16247-3
Online ISBN: 978-3-642-16248-0
eBook Packages: Computer ScienceComputer Science (R0)